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Properties

Label 3.56.112.2.1
Class number $2$
Dimension $3$
Determinant $56$
Level $112$

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Lattice Invariants

Dimension:$3$
Determinant:$56$
Level:$112$
Density:$0.197901735287287658130770882991\dots$
Group order:$8$
Hermite number:$0.522757958574710216748296187159\dots$
Minimal vector length:$2$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{2} \) \(\mathstrut +\mathstrut 4 q^{4} \) \(\mathstrut +\mathstrut 8 q^{8} \) \(\mathstrut +\mathstrut 4 q^{10} \) \(\mathstrut +\mathstrut 8 q^{12} \) \(\mathstrut +\mathstrut 2 q^{14} \) \(\mathstrut +\mathstrut 20 q^{16} \) \(\mathstrut +\mathstrut 2 q^{18} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 4 & 0 \\ 0 & 0 & 8 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$2$
 
$\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 4 & 0 \\ 0 & 0 & 8 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 1 \\ -1 & 4 & 0 \\ 1 & 0 & 4 \end{array}\right)$
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Comments

This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.